MRF Parameter Estimation

Abstract

A probabilistic distribution function has two essential elements: the form of the function and the involved parameters. For example, the joint distribu­tion of an MRF is characterized by a Gibbs function with a set of clique potential parameters; and the noise by a zero-mean Gaussian distribution parameterized by a variance. A probability model is incomplete if the in­volved parameters are not all specified even if the functional form of the distribution is known. While formulating the forms of objective functions such as the posterior distribution has long been a subject of research for in vision, estimating the involved parameters has a much shorter history. Generally, it is performed by optimizing a statistical criterion, e.g. using existing techniques such as maximum likelihood, coding, pseudo-likelihood, expectation-maximization, Bayes.